Performance of Ejectors As a Function of the Molecular Weights of

PERFORMANCE OF EJECTORS As a Function of the Molecular Weights of Vapors LINCOLN T. WORK AND VINCENT W. HAEDRICH' Columbia University, New York, N. Y.

F

OR many years ejectors have been used extensively in power generating plants and have found wide application in the chemical industries. They utilize the energy of velocity in a fluid to effect entrainment and may be operated with liquids, gases, or vapors. I n present practice, steam and compressed air ejectors have an important place in the field They are fundamentally simple in design and reliable in service, and they operate with cheap, readily available fluids. In power plant practice they are used principally in exhausting air from condensers and in priming pumps. I n the chemical industries they are utilized in vacuum evaporation, filtration, compressing air for agitation, and in the pumping of solids, liquids, and gases. Within the past few years their scope has been greatly broadened by application to the field of refrigeration. Refrigeration in a n ejector system is accomplished by the evaporation of a liquid a t low pressures, produced by the kinetic action of a jet. The amount of cooling is equivalent to the latent heat removed in the vapor formed. The cost of energy is based on the heat required to produce pressure vapor in a boiler. However, the cost per unit of refrigeration is dependent upon the effectiveness of the ejector. The latter must be designed to meet rigid requirements imposed by the physical conditions of the system. I n present commercial practice steam and water are used almost exclusively. It was thought possible that a more economical and effective system could be devised by using other fluids, even to the extent of utilizing a combination of substances. I n spite of the success of the ejector in practical application, the process of entrainment remains one of the complex problems of fluid dynamics. The energy of the jet stream and the interchange of momentum constitute the present bases on which 'fundamental analysis of ejectors rests. This gives little information for design, and by far the greater part of the design problem remains empirical. Undoubtedly further development in ejector refrigeration can be accomplished through improvement in ejector design. However, the use of other fluids appears promising as a means of making substantial advance in ejector performance. For a given pressure drop across the jet, the molal kinetic energy of the fluid should be essentially constant, regardless of fluid because of the fact that the velocity will change in inverse ratio to the square root of the molecular weight, while the mass will be proportional to the molecular weight. On the other hand, the molal momentum of the jet fluid will change roughly in proportion to the square root of the molecular weight, and a large molecular weight will give more available momentum than a small one. A number of questions remain unanswered, however, even in the light of this concept. The first of these pertains to ejector design-whether with a change of fluid a change of design will be necessary. More

significant is the question of whether all fluids will behave alike, and particularly of how these different fluids will behave on the entraining side of the jet. It was in the hope of answering some of these questions that this study was undertaken.

Vapors with molecular weights from 18 to 154 have been tested in two commercially available ejectors to determine the performance characteristics of several combinations. Curves of suction us. boiler pressure for different exhaust pressures show that all vapors behave similarly in a given ejector. This has been further correlated by means of the Carnot efficiency of compression compared with that of expansion, and a single line results for an ejector regardless of the nature of the fluid or the exhaust pressure. Entrainment relations for self-entrainment-that is, the same fluid in the boiler and in the evaporator-and for twocomponent systems have been studied; an expression has been derived for the amount of entrainment in terms of molecular weight ratios. Characteristics of an ejector are defined in terms of certain pressure characteristics so that the performance w i t h any fluid combination may be predicted from the performance data on the steam-water vapor system. The relation of this work to the use of ejectors on stills and in air-conditioning systems is indicated. With respect to air-conditioning systems, substantial savings appear possible when suitable molecular weight ratios and pressure conditions are used; an improvement from 75 to 200 per cent is possible, but the result is often a degenerate system from which recovery is costly. Requirements for systems avoiding this difficulty and offering opportunity to effect savings are noted.

The selection of substances involved several different types of molecular structure, ranging in molecular weights from 18 to 154. Discharge values for the ejector nozzles were experimentally determined for the condensable fluids employed; and where thermodynamic data were available, these values were also calculated. The entrainment systems investigated are classified into self-entrainment and two-component entrainment. The former involves the use of identical primary (boiler) fluid and

1 Present address, E. I. du Pont de Nemours & Company, Ino., Wilmington. Del.

464

APRIL, 1939

INDUSTRIAL AND ENGINEERING CHEMISTRY

secondary (suction) fluid. I n the two-component system the primary and secondary fluids are different chemical substances. The use of two-component entrainment with self-entrainment as a special case enabled the development of relations for quantities and for heat requirements under various pressure conditions. I n this study two commercially manufactured ejectors, each designed for a different ratio of compression and of a size suitable for laboratory experimentation, were employed. They are each of the single nozzle type and circular in cross section. The purpose of this investigation, then, is to establish relations on a molecular weight basis and to determine the characteristics of a n ejector when used with various vapor systems. It is hoped that the findings may be put t o advantage in further research directed toward practical application. The importance of a comprehensive study t o the chemical industries using ejectors should not be minimized. However, it is with the thought that further advances in ejector refrigeration may be made that this study has been undertaken. The literature in this field indicates results of experimental studies, theoretical consideration of ejector structures for the best entrainment, and thermodynamic analysis of potential ejector systems. At the time Sir Charles Parsons suggested refrigeration by means of a steam ejector, ejector design was not sufficiently developed for commercial application; but improvements in the past thirty years have brought the ejector to a state of commercial usefulness. A two-component system using mercury in the boiler and water in the evaporator was proposed by Whitney (26). Mellanby (15) and Watson (26) made experimental studies of the structural relations between the nozzle and the diffuser. Kalustian (11) studied the self-entrainment systems of trichlorethylene and other fluids from the thermodynamic viewpoint but offered no experimental evidence to justify his conclusion. Other studies have been reported in the literature (1-5, 8, 9, 10, 16,IS, 16, 17, 18, ,%'l-24, 27).

Equipment The equipment used in the experimental work is illustrated in Figure 1 but was modified to fit the structure of each ejector. The two ejectors (manufactured by Schutte and Koerting Company) are shown in Figure 2. The fluid flow paths and the general constructional elements are different in each. The dimensions are accurate only in so far as it was possible to make measurements without cutting the ejectors into sections. The equipment consists of a 2-gallon steam-jacketed autoclave, A , with an inner steam coil, which served as the boiler for the primary vapor. When steam or air was used, the equipment was disconnected at the autoclave opening and reconnected direct to the supply line. A strainer was employed when steam was the primary fluid. Vapor flowed through a '/&-inchmagnesia-insulated line, B, to a needle valve, C, for regulating the primary vapor pressure. The line continued in a double bend, D,submerged in an oil bath, E, which was heated by a Bunsen burner, F . From this point it continued t o the ejector, J. Primary vapor pressure and vapor line temperature were recorded by a Bourdon gage, H , and a mercury thermometer, I, set in a thermometer well. The latter was placed in the line between the gage and the ejector. A mercury thermometer, G, recorded the oil bath temperature which was held at a point sufficiently above saturation to keep the vapor line dry. This was important in preventing liquid surges into the nozzle and assuring continuity of flow. It was accomplished by heating the bath slightly above saturation temperature while the pressure in the line was held constant. When the pipe walls became dry, the temperature at I would slowly begin to rise. After a rise of a few degrees, the bath temperature was maintained at that point during the run. With this method of heating, the superheat of the vapor did not exceed about 10 F. above saturaO

465

tion temperature. However, equilibrium saturation temperatures a t boiler pressure were used in computation because the velocity of the jet quickly causes normal dew formation. Had the temperature rise been as much as 20" F. with steam, the heat of the vapor would have increased only one per cent over the latent heat. To ensure the correctness of the pressure readings, gage H was calibrated twice during the test runs by means of a hydraulic test machine and was found to have maintained its accuracy. Thus the readings recorded by the gage were the actual pressures a t the nozzle approach within the limit of precisionrof the gage (0.5 pound per square inch).

FIGURE 1. DIAGRAM OF EQUIPMENT

A 1-liter magnesia-insulated steel vessel made of 3-inch capped pipe, 0, provided with a Bourdon gage, P , was used to generate secondary va or. Heat was applied under the vessel by a flat burner, Q. wet-type displacement meter reading to 0,001 cubic foot was substituted for the steel vessel when air was the secondary fluid. The vapor discharged into an insulated suction line, L, fitted with a needle valve, N , for regulating the pressure and a mercury manometer, M , for measuring it. In every case it was found t o be insignificant. Thus the readings recorded by manometer M may be considered the true pressure of the secondary fluid. The ejector discharge was connected direct to the condenser, K. The condenser consisted of 8 feet of 6/8-inch seamless copper tubing fitted into a 3-inch capped pipe, 20 inches in length. When the large ejector was used, a lar er condenser made of 20 feet of 1-inch copper tubing was emaoyed. The condenser outlet was connected t o an oversize three-way plug cock, R, used to direct the condensate to reservoir X or to a sample flask, T. The reservoir was used t o collect the condensate while valve settings were being made. After steady conditions were attained, the three-way cock was turned and the condensate collected in a sample flask. The reservoir was fitted with a siphon tube and a stopcock, U , for removing the condensate on the completion of a run. A two-way cock, V , was used to maintain a vacuum in the system when the sample flask was being removed. It was necessary to measure the pressure against which the ejector was discharging. Because of possible condensation in any measuring device placed inside the condenser, it was inadvisable t o determine pressures at this point. Therefore, a mercury manometer, W , for measuring the exhaust pressure was set in the line beyond the condenser outlet. Reduced exhaust pressures were maintained by a water jet pump and were regulated by an air vent, X . An overflow receiver, Y , was fitted into the line as shown. The vapor lines chosen for experimentation were all oversize, and a check made on the location of the meters showed that the established location read true values within the precision of the instrument.

1


466

Experimental Studies The equipment was used to establish various relations of ejector performance. Nozzle discharge a t a given boiler pressure was determined for steam, methanol, ethanol, benzene, and trichlorethylene in the small ejector, and for steam, methanol, and benzene in the large one. Determinations were made by regulation of valve C for the proper pressure as recorded by gage H. Pipe wall dryness was ensured by the method already described. Suction valve N , by which the secondary fluid would normally enter, was kept closed during this series of runs. Condensate from the primary vapor was allowed to flow into reservoir ,

FIGURE 2. EJECTOR DETAILS Measurement

Small Ejeotor

In.

In.

Over-all length Nozzle length Diffuser length Nozzle throat diameter Nozzle mouth diameter Diffuser throat diameter U. Diffuser exhaust diameter

1.55 0.35 1.29 0.063 0.099 0.125 0.203

3.59 1.67 2.03 0.104 0.203 0.250 0.343

A. B. C. D. E. F.

Large Ejeotor

S a t atmospheric exhaust pressure until steady conditions were established; then, by turning stopcock R, the condensate was directed to sample flask T. The time of flow was measured by a stop watch and the condensate weighed to the nearest half gram. Individual determinations checked the average within a t least one per cent; in most cases the agreement was even better. Boiler pressures studied in the small ejector ranged from about 25 to 65 pounds per square inch absolute, and in the large ejector, up to 90 pounds per square inch absolute. The relations between the boiler pressure, exhaust pressure, and suction pressure a t zero entrainment were determined for steam, air, methanol, ethanol, benzene, and trichlorethylene in runs exhausting to atmospheric pressure in the small ejector. Steam, methanol, and trichlorethylene were used in runs exhausting to reduced pressures. The relations were. determined for steam, methanol, and benzene in the large ejector. The three pressures studied are mutually dependent in a given ejector; if two are fixed, the third is automatically established. Thus in the experimental work, relations were determined by holding one pressure constant, varying a second, and thereby fixing the third, When exhausting to atmospheric pressure, the exhaust pressure was maintained constant and suction valve N was kept closed as the boiler pressure was varied. Pressure readings were taken on gage H and manometer M in these runs. When exhausting to reduced pressures, the boiler pressure read on gage H was maintained constant, and suction valve N was kept closed as the exhaust pressure was varied. Pressure readings were taken on manometers M and W in these runs. Sufficient data were determined to establish the variation in each case. Suction and exhaust ressures were maintained within a t least * 5 mm. of mercury 6 . 1 pound per square inch) of the mean. Boiler pressures were maintained constant within the limit of observation of gage H . Boiler pressures studied in the small ejector ranged from about 25 to 85 pounds per square inch absolute, and in the large ejector, up to 115 pounds per square inch abso-

VOL. 31, NO. 4

lute. Exhaust pressures studied ranged from atmospheric down to about 3 pounds per square inch absolute. Entrainment relations were established for steam, air, methanol, ethanol, benzene, and trichlorethylene as primary fluids in the small ejector, and for steam, methanol, and benzene in the large one. These substances were also used as secondary fluids in the small ejector; in addition, ethyl ether, carbon disulfide, chloroform, and carbon tetrachloride were employed. Steam, air, methanol, benzene, and carbon tetrachloride were used as secondary fluids in the large ejector. Both self-entrainment and mixed-entrainment systems of various fluid combinations were investigated. Entrainment was studied as a function of suction pressure under various fixed boiler and exhaust pressure conditions. In determining the relation for a given system, suction valve N was kept closed until steady boiler and exhaust pressures were attained as measured by age H and manometer W , respectively. Suction valve N was tken opened slightly; this increased the suction pressure and allowed entrainment of a small amount of secondary fluid. After a sample was collected for test, suction valve N was opened slightly more and another determination made. Steady conditions were established at each suction pressure before the condensate was collected and tested as outlined below. Sufficient data were taken to determine the relation in each case. Maximum variation in suction pressure from the mean during collection was about 6 mm. of mercury (0.12 pound per square inch) and in most cases was maintained within 2 or 3 mm. of the mean. Exhaust and boiler pressures were maintained within the same limits as in the ressure relation tests. It was possible to duplicate results witgin a maximum of 5 per cent. Boiler pressures studied in the small ejector ranged from abput 25 t o 65 pounds per square inch absolute and, in the large ejector, up to 90 pounds per square inch absolute. Exhaust pressures studied ranged from atmospheric down to about 3 pounds per square inch absolute. An analysis of the condensate was made'according to its composition. In a single-component system the difference in weight per unit time between the condensate and nozzle discharge was determined and calculated as the pounds of secondary fluid entrained per hour. Condensate was collected and measured in the same manner as in nozzle discharge tests. Nozzle discharge was determined in all entrainment runs by collecting, timing, and weighing at least three separate samples a t the boiler pressure used in entrainment. I n a two-component system where the fluids were miscible (as methanol-water, ethanol-water, methanol-carbon tetrachloride, benzene-chloroform, etc.) the composition of the condensate was determined by specific gravity measurement. The pounds of secondary fluid entrained per hour were obtained by multi lying the nozzle discharge by the ratio corresponding to the specitc gravity of the condensate. In the two-component system where the fluids were immiscible and se arated into well-defined layers (as benzene-water, trichloretiylene-water, and carbon tetrachloride-water) condensate was collected in 100-cc. graduated cylinders in which the total volume was measured. The volume of each component was determined by centrifuging the condensate in graduated tubes. Multiplication of the volume by the respective specific gravities yielded the weight of each component. The pounds of secondary fluid entrained per hour were obtained by multiplying nozzle discharge by the weight ratio of secondary to primary fluid, the nozzle discharge being known for the conditions of the experiment. When air was used as secondary fluid, a wet-type displaoement reading to 0.001 cubic foot was substituted for the evaporator. Air temperature and pressure were noted, and the equivalent weight was determined by the use of air tables (19). Values were reported as pounds of air entrained per hour. When air was used as the primary fluid, entrainment was timed by a stop watch and measured as the difference in weight of secondary fluid in the eva orator before and after the run. No condensate was collected $wing these runs for use in measuring entrainment.

Nozzle Discharge and Suction Relations An ejector serves to permit the expansion of a pressure vapor through a nozzle across a zone of low pressure to a region of intermediate pressure. During the expansion the pressure vapor acquires considerable kinetic energy which may be put to useful work. Part of this energy is utilized in the entrainment of a secondary fluid, part is used to compress the mixture t o exhaust pressure in a tailpiece or diffuser, and the rest is lost. If the flow of secondary fluid is reduced by throttling the suction valve, less energy is utilized for en-

APRIL, 1939


trainmeni,. Then the energy available for compression is increased, and compression over a wider range of pressures becomes possible. For a fixed exhaust pressure, the net result is a n increased vacuum. When the suction valve is closed, entrainment of secondary vapor becomes zero and vacuum is a maximum. An investigation into this limiting region was undertaken in order to establish maximum suction with given pressures of boiler and exhaust and with different inolecular weights of fluids. The quantity of flow through the nozzle is controlled primarily by boiler pressure and the molecular weight of the fluid. By operating under conditions of no entrainment, it was possible to measure the actual flow through the nozzle for different boiler pressures and to measure the suction pressure which resulted. All of the tests were operated above a critical pressure ratio so that the discharge characteristics of the nozzle were not affected by the degree of suction prevailing. Where thermodynamic data were available, discharge was computed according to well-known relations (IC),and it was found that the actual flow was about 1 to 5 per cent less than the theoretical flow. The average coefficient for the small ejector is 0.958 * 1.9 per cent, and in the large ejector the average coefficient is 0.985. A number of different exhaust pressures were used to determine how suction pressure was affected by exhaust pressure. The variation of suction pressure with boiler pressure is presented graphically for the small ejector in Figure 3 and for the large one in Figure 4. Each curve represents the variation for a fixed exhaust pressure. All curves are of the same general shape, irrespective of absolute pressures, ejectors, or substances used. As the boiler pressure is increased above exhaust pressure, a reduction in suction pressure takes place a t an increasing rate to the critical pressure ratio which is sketched for steam on the graphs. Above this ratio the curves continue in essentially straight lines, which indicates a constant reduction of suction pressure with unit increase in boiler pressure. The same slope is maintained down to a minimum suction pressure. Any further increase in boiler pressure beyond this minimum causes an increase

0.01

0

I

20

-

I

40

I

60

I

80

467

in suction pressure. Maximum vacuum can be attained only a t a n optimum flow rate which is different for each exhaust pressure and design of ejector. Of even greater significance is the fact that all vapors, irrespective of molecular weight, show a striking similarity in behavior. For example, five condensable vapors ace shown in Figure 3 when exhausting against pressures ranging from 14.5 to 14.9 pounds per square inch in the small ejector. All five follow the same pattern in a very narrow band all the way from maximum suction pressure to the minimum and beyond. This has also been found to hold for steam, methanol, and trichlorethylene when exhausting to reduced pressures in the small ejector, and for steam, methanol, and benzene exhausting to atmosphere in the large one. Even air, a noncondensable gas, follows the same general trend, but in this case the minimum is somewhat lower and the corresponding boiler pressure somewhat higher. The boiler pressure causing minimum suction pressure diminishes with diminishing exhaust pressure in such a relation that A / P , is a constant of 4.0 for the small ejector, and 5.5 for the large one; P0/Pz is 1/3.7 for the small ejector and 1/7.3 for the large one. While such a relation is known to exist for a single fluid such as steam, the experimental work in the present study shows that it is independent of molecular weight. Figure 3 shows that the condensable vapors exhausting to atmosphere have two minima, one about a pound per square inch lower than the other. The corresponding boiler pressure is about 4 pounds per square inch higher. The region near these points is metastable. After the higher suction pressure is attained, operating conditions may be maintained constant during observation of the suction manometer. Without warning the pressure will suddenly decrease to the lower value. The higher suction pressure can be reattained by lowering the boiler pressure below the first minimum point and then gradually approaching it again. By increasing the boiler pressure above the minimum and then gradually lowering it, the lower equilibrium suction pressure can be attained. This phenomenon is probably due to supersaturation. In a normal adiabatic expansion, vapors tend to con-

I

BOILER PRESSURE POUNDS PER SQUARE INCH ABS. FIGURE3. SUCTION RELATIONS IN SMALL EJECTOR FIGURE4.

SUCTION RELATIONS IN LAFWE EJECTOR


468

VOL. 31, NO. 4

=J.U

METHANOL w

10

A

BENZENE

0

ETHANOL

Q? Ly

=! 0

m

LB/SQ.IU8.00 10.20 I 2.70

8.1s

11.91 10.00

65

8.36

11.76 11.30

AT%

POUNDS OF SECONDARY VAWR ENTRAINED PER HOUR FIGURE 6. SELFENTRAINMENT IN SMALL EJECTOR

N =

FIGURE5. EFFICIENCY CORRELATION AT ZERO ENTRAINMENT IN BOTH EJECTORS

dense as velocity head is acquired. However, because of the rapidity of expansion, condensation may not occur (7). The vapor is then said to be supersaturated, in which case it behaves more like a gas. This may explain the tendency of the lower minima to simulate air more nearly than do the higher ones. Here again in this region of metastability, striking sirnilarit,y is noted among the several vapors which even behave alike when there is a variation from the regularity of performance. With this method of plotting where kinetic concepts dominate, linear relations are obtained for various exhaust pressures and these may be further correlated into a single functional relation for a given ejector by thermodynamic analysis. The simplest cycle which can be used in analyzing ejector operation is the ideal Carnot cycle, and although an ejector normally operates according to the Rankine cycle, the differences in efficiency are small (about 3 per cent). Hence the simpler function of Carnot efficiency may be used. I n the Carnot cycle the over-all efficiency can be expressed as the ratio of the efficiency of compression to that of expansion, which in terms of absolute temperatures becomes Tb(T, - To)/Tz(Tb- TO). The energies of compression and expansion can be expressed as functions of the operating pressures, and the ratio P,/Pz, boiler to exhaust pressure, has been taken for this purpose. This may be partially justified by the usual kinetic equations i’n which heat changes are shown to be functions of the ratios of compression, PJPo, and expansion, Pb/Pz. If a ratio of the former to the latter is taken, the ratio Pz/Powhich results should be a function of the over-all efficiency. The functional relation which justifies this may be derived from the following well-known equations (21):

where To= absolute saturation temperature at zero entreinment J = mechanical equivalent of heat The resulting ratio of Equation 1 to Equation 2 or the overall efficiency shows the relation among the three pressures:

Since these pressures have been shown to be mutually d e pendent in ejector operation, Po can be eliminated from the equation, which then becomes a functional relation of the efficiency, E = f(ps/pb) or its inverse ratio, f’(pb/pz). Carnot efficiencies and pressure ratios have been computed for all experimental readings. The relation between efficiency and pressure ratio in the two ejectors is presented graphically in Figure 5. The efficiency increases with the ratio to a point where a maximum is attained; beyond this point the normal curves show decreasing efficiency with increasing ratio. Further increase in pressure ratio causes a reduction in efficiency. The maximum efficiency on this curve corresponds to the several minima on Figure 3. A second maximum representing the metastable position is noted in the correlation graph. Maximum deviation of the maximum efficiencies from the mean in the small ejector is about *3.5 per cent and is even less in the large unit. Thus in the limit as entrainment approaches zero, an ejector operates just as efficiently with one vapor as another. M o r e over, the efficiency is the same function of the ratio of boiler to exhaust pressure, irrespective of the fluids used over the entire range of pressures studied. This method of representation is therefore a basis for correlating any single ejector with

APRIL, 1939


respect to the range of pressure conditions when operating with all vapors, irrespective of their molecular weights.

469

where W = weight discharge of primary fluid in unit time w = weight of secondary fluid entrained in unit time VI Vs = primary fluid velocities before and after impact, respectively 1

Entrainment The subject of entrainment has been divided into two phases: the specific case of entrainment in a single component system-i. e. self-entrainment-and the more general case in which different fluids are used in the boiler and in the evaporator-i. e., two-component entrainment. I n either case the basic method of achieving entrainment is the same. When an ejector is operating under definite pressures of boiler and exhaust, and suction or secondary fluid is admitted, the motivator or primary fluid no longer passes unimpeded through the entrainment zone but impinges against the secondary molecules. I n accordance with the concept of conservation of momentum, the latter gains momentum equivalent to that lost by the former, and the total momentum before and after impact remains constant. This concept may be reduced to the form of an equation:

wv1 =

(W

+ w)V*

The kinetic energy of the system before impact may be measured in terms of W V I 2 and , after impact in terms of (w W ) V Z 2 .From the momenturn equation, the velocity before impact is greater than that after and therefore the kinetic energy of the jet is greater than that of the mixture. The difference between the two is impact reheat which is absorbed by the vapor and probably serves in revaporizing dew formed on expansion. Thus, the amount of entrainment is a function of both the original kinetic energy and the interchange of momentum. As the amount of the entrainment increases, the absorption of kinetic energy in interchange of momentum and reheat yields a kinetic energy per unit weight for the combined primary and secondary vapors which is less than the original kinetic energy per unit weight of the jet. Hence the amount of compression will decrease with increasing entrainment, and for a given exhaust pressure the suction pressure will rise. With this brief discussion of

+

Courtssu. Elliot Company

A THREE-STAGE BOOSTER EJECTOR UNITMAINTAINS THE HIGHVACUUM NECESSARY FOR THE SUCCESSFUL OPERATION OF EACH OF THESE IN A REFINERY FOR EDIBLE OILS DEODORIZERS


470

mechanism, the experimental work w ill be presented under the headings of Self-Entrainment and Two-Component Entrainment.

Self- Entrainment Beginning with any set of suction conditions which represents zero entrainment when operating with any primary fluid, secondary fluid of the same composition may be admitted in various amounts, and a number of entrainment relations may be established in which molecular weight of the fluid used becomes a factor. This is the simplest system of entrainment and provides a basis for later study in the more complex field of two-component entrainment where the primary and secondary fluids are different. If secondary fluid is admitted to the suction chamber at a pressure below exhaust but above the suction pressure at zero entrainment, the jet will cause entrainment and the amount of that entrainment will vary with the suction pressure which exists. Conditions between the critical pressure and minimum suction pressure were selected for experimental study, and an extensive number of runs were made on the small ejector as well as a few to check the relation on the large one. Boiler and exhaust pressures were maintained constant during a run, while suction pressure was varied by admitting secondary vapor in increasing amounts. The total condensate was collected and measured over a definite time interval a t each suction pressure. Nozzle discharge previously determined was subtracted from the total condensate to give the amount of entrainment a t each pressure. The results of these runs are presented graphically in Figure 6. Suction pressures in pounds per square inch absolute are plotted as ordinates against pounds of evaporator fluid entrained per hour. When the zero entrainment points on these graphs are on the straight portion of the pressure relation curves (Figures 3 and 4), the amount of entrainment increases with increasing suction pressure in straight-line relations. The benzene

= Px - Pe Px - Po

I

I

\

&.70

\

\"

,c=.so

EJECTOR S

L A R G E - D A S H LINE SMALL-561lD LINE

VOL. 31, NO. 4

In order to establish a correlation, the velocity and energy considerations for the self-entrainment case may be amplified beyond the general considerations already given. The velocity acquired in expanding through the nozzle is dependent upon the energy of expansion according to the general relation: V = 224 AH.(^

where V

-

y)]'/2

nozzle discharge velocity, ft./sec. A H , = heat of expansion from boiler to suction pressure, B. t. u./lb. y = reheat, generally taken as 15 per cent =

For simplicity, assume that the secondary fluid just before entrainment has zero velocity in the direction of flow of the primary fluid. I n order to raise its velocity to that of the entraining jet, a n expenditure of wAH,(l - y) B. t. u. is required (where w represents the pounds of secondary fluid entrained per hour). However, because kinetic energy is required to develop velocity in the secondary fluid, w never acquires the original velocity of the jet except when entrainment approaches zero. Since under the conditions of iniinitesimal entrainment the amount of energy available for entrainment is W A H e ( l - y), the efficiency of entrainment becomes wAH,(l - y ) / W A H . ( l - y) or simply w / W . On compression, the useful work done is (w W ) A H , , where AH, is the heat of compression from suction to exhaust pressure; and as the energy available for compression is (w W ) A H e ( l - y), the efficiency of compression becomes A H o / A H e ( l - y). The combined efficiency of entrainment and compression is therefore E,, = wAHc/WAHe(l- y)

+

+

and the over-all efficiency of expansion, entrainment, and compression is Eo w A H ~ / W A H ~ Since AHc and AH, are functions of the ratio of compression, PX/Po,and the ratio of expansion, Pb/Po, respectively, the efficiency becomes a function of Px/Pb: EO = f(wPz/WPb)

However, this is true only when w approaches zero. It must be modified to apply when finite entrainment conditions exist. It has been shown that the suction pressure a t zero entrainment, Po, is a function of both exhaust and boiler pressures and that all three are mutually dependent. Therefore, if the pressure of finite entrainment is chosen in a definite relation to Po and either of the other pressures, the efficiency of actual operation is another function of the same expression: E = fl(WPz/WPb)

When the efficiency is a constant, the weight ratio then becomes a function of the inverse pressure ratio: \

k/W=WEIGHT kATIO-SECONDj\RY TO'PRIMARY VAPOR = M O L A L RATIO=Z/W

.I

.2 .3 .4 .s .6 .7 .8 .9 C FOR SELF-ENTRAINMENT FIGURE 7. FACTOR

'curves are typical of this variation. As the minimum suction pressures for zero entrainment are approached, the curves show a higher rate of entrainment which decreases until a uniform rate is attained as illustrated by steam curves 1, 3, and 5 . This transition point is represented by a value of Pb/Pz of about 3.9 for the small ejector. The curves resemble those given in the literature and in commercial publications, but the latter are limited to steam and air (6,16, 2c, 21).

w/w

f"(pb/pz)

Several functions of the various pressures might have been taken in a correlation designed to define completely a basic entrainment pressure. However, one employing exhaust pressure was devised to meet the need of simplicity and logic. The difference between exhaust pressure and entrainment pressure represents the compression range during any finite entrainment. Similarly, the difference between exhaust and suction pressure a t zero entrainment represents the maximum compression range possible when operating under fixed boiler and exhaust pressure conditions. The ratio of the former to the latter, then, is the percentage of compression possible a t any entrainment level relative to the maximum attainable. In the conventional symbols, ratio C = ( P , - P e ) / ( P z- PO)

APRIL, 1939


Since the suction pressure, P,, increases with entrainment, and other terms of the equation remain constant, the whole ratio decreases with increasing entrainment. The results of a correlation on this basis are presented. If weight ratio w / w is plotted against pressure ratio Pb/Pz, under entrainment conditions defined by a constant ratio, C, a continuous curve is obtained. I n F i g y e 7 such a plot has been made for data on both ejectors. Three curves corresponding to values of C equal to 0.70, 0.50, and 0.35 are shown for the small ejector, and two corresponding to values of C equal to 0.70 and 0.50 are shown for the large ejector. They represent all the vapors used in the study. I n obtaining these curves, the entrainment pressure was first computed by substituting values of P, and Po in the C equation. The corresponding weight of secondary fluid was obtained from the curves of Figure 6 and divided by the weight of primary fluid employed to give the ratio w / W , which is equivalent to the molal ratio, The average deviation of these values from the mean is less than k 2 . 5 per cent. Therefore, the weight ratio of secondary fluid entrained to primary vapor employed is the same, irrespective of molecular weight for all fluids in self-entrainment a t the same ratio of boiler pressure to exhaust pressure when entrainment pressure is obtained according to the method outlined. The range of conditions covers those which would ordinarily be encountered in actual practice. The correlation is effective only for values in the normal operating region of the ejector. It cannot be used above PJP, representing minimum suction pressure or in the region of metastability, and it has not been tested for pressure below the critical. The atmospheric boiling points of the different fluids used vary from 66" to 100" C., and a t reduced and elevated pressures they varied considerably on either side of these values. Thus variation in boiler pressure does not appear to be a significant factor, but it may be a useful factor in the selection of a refrigerant. Advantage may accrue in self-entrainment systems through the use of fluids, the vapor pressures of which for the desired suction and available condenser temperatures give more favorable compression ratios than the present steam-steam system. As was indicated in the development of the self-entrainment relation, the weight ratio is a function of the pressure ratio only when the efficiency is a constant. Since a continuous relation has been shown to exist, any point on the curves of Figure 7 represents a single efficiency. Therefore, when operating under conditions determined by a constant ratio of pressure differences, C, all fluids in self-entrainment perform with equal effectiveness, irrespective of molecular weights. It is more than significant that such a striking similarity in performance exists in spite of the wide variation of physical properties exhibited in the investigation of the several fluids used. It indicates that a fundamental balance of the factors involved in expansion, entrainment, and compression has been achieved in the relation developed.

471

w/%.

Two-Component Entrainment When one vapor is used to entrain another, the relations which exist are more complex than in self-entrainment by reason of differences in the properties of the two fluids. The combinations of fluids possible in such a study is almost unlimited, but the choice of only a few representative combinations based on molecular weights was considered sufficient to cover the greater part of all possible systems. Several substances ranging in molecular weight from 18 to 131 were selected for primary fluids, and substances ranging in molecular weight from 18 to 154 for secondary fluids. Each primary fluid was used to entrain several secondary fluids over a wide range of pressures. Thus many combinations were tested

FIGURE 8. TWO-COMPONENT ENTRAINMENT IN SMALL EJECTOR

where light molecules were made to entrain heavy ones, heavy ones to entrain light ones, and many intermediate cases. Since performance varies over the range of operating pressures in a n ejector, it was necessary to study two-component entrainment for each primary fluid when entraining several secondary fluids a t fixed boiler and exhaust pressures. One or more sets of entrainment curves were obtained for each primary fluid used in each ejector. A summary of these sets showing the operating pressure conditions and the secondary fluids entrained is given in Table I. A representative set of curves has been selected for each primary fluid and is presented graphically in Figure 8. The same quantities are plotted as in the self-entrainment graphs of Figure 6. The curves are arranged according to increasing molecular weights of the primary fluid-steam, methanol, ethanol, benzene, and trichlorethylene. The percentage spread a t constant suction pressure between any two given secondary fluids increases as the molecular weight of the primary fluid increases. This general observation holds not only for the sample runs illustrated in Figure 8 but for all other runs, regardless of the suction pressure for zero entrainment. Molal entrainment, which can be simply computed from weight entrainment, represents a more useful basis of comparison than weight, particularly for heat efficiency studies in which the Trouton rule may be utilized. It has been found in this study that when the molal entrainment of various secondary fluids, as shown in Figure 8 for a single series of runs, is plotted against their molecular weights on logarithmic paper, for any given suction pressure, a straight line results. Moreover, when more than one set of curves has been investigated for any primary fluid, the lines are parallel. This correspondence not only holds over the entire range of operation of an ejector but also applies to other ejectors as evidenced by the fact that the series of runs made with the large


472

ejector using steam and methanol give logarithmic curves paralleling the respective curves for the small ejector. The single exception to these relations is the noncondensable gas, air, which gives a slightly curved line. TABLE I. SYSTEMS O F ENTRAINMENT O F VARIOUS FLUIDS UNDER UNIFORM CONDITIONS Primary Fluid

P,

Pa

Pb

-Lb./eq.

Steam ,Steam Steam Steam Methanol Methanol Ethanol Benzene Trichlorethylene Trichlorethylene Air Air

Small 30.7 42.8 64.7 42.7 44.8 33.7 44.2 41.9 40.6 34.0 45.3 60.2

Steam Methanol

Large Ejector 90.7 2.11 9.31 59.5

-

Secondary Fluida"

in.-

Ejector 11.11 7.02 3.75 3.10 7.35 2.10 7.70 8.39 8.87 2.74 6.99 3.23

Atm. Atm. Atm. 10.20 Atm. 8.12 Atm. Atm. Atm. 8.36 Atm. Atm. Atm. Atm.

s a,b,c &b,o

5 a = . air, b benzene, c = carbon tetrachloride d = oarbon disulfide, e = ethanol, et = ethyl ether, h = chloroform, m 2 methanol, 8 = steam, t = trichlorethylene.

A representative plot for each primary fluid is given in Figure 9 to show the relation between the molecular weight of the secondary fluid and molal entrainment for each primary fluid. Each point on a given curve represents entrainment a t a single suction pressure when operating under fixed boiler and exhaust pressures. Suction pressures have been chosen arbitrarily, but the same slopes result, no matter what pressures are taken. The curves of Figure 8 show an increasing tendency to spread with increasing molecular weight of primary fluid when plotted on a weight basis. If these curves had been plotted on a molal basis, the tendency to spread would have been reversed; i. e., the greatest spread would have been experienced with the primary fluid of lowest molecular weight. This is reflected in the logarithmic curves where the slope increases with decreasing molecular weight of primary fluid. The mathematical relations corresponding to the curves of the type represented by the condensable vapors may be easily derived. The equation of a straight line on logarithmic paper takes the form:

VOL. 31,NO. 4

Substituting this value in the original equation: =

-10-0.0084M

No effort was successful in establishing relations for the value of c, but the relation here developed permits computation of two-component entrainment for a given ejector from a single set of test values at the same boiler, suction, and exhaust pressures. Figure 9 brings out several significant characteristics of the performance of ejectors. As the molecular weight of the primary fluid increases, the numerical value of -N decreases; or if the curve is extrapolated, N approaches zero a t high molecular weights. When N equals zero, W equals cmo. Since any value of m raised to the zero power equals unity, ;iE approaches a constant value for secondary vapors as the molecular weight of the primary vapor approaches very large values. As the molecular weight of the primary fluid decreases, the numerical value of - N increases. This indicates an increasing spread in the capacity to entrain two fluids of different molecular weights. When the molecular weight of the primary fluid approaches zero, N approaches -1.0. Consequently, if a theoretical primary fluid of zero molecular weight were used, molal entrainment would be inversely proportional to the molecular weight of the secondary fluid. Thus the relations which exist over the whole range of molecular weight combinations in two-component entrainment of condensable vapors have been established. 2W

-SMALL

EJECTOR

---LARGE

EJECTOR

w = CrnN

Constant c is determined by the construction of the ejector and by the operating conditions. Exponent N is determined by the slope of the curve, and so its value is a function of the molecular weight of the primary fluid. Since the slopes decrease negatively with increasing molecular weight, N also decreases with increasing molecular weight. In a correlation of these factors, a straight-line relation on semilogarithGc paper has been found to exist when N is plotted on the logarithmic scale against the corresponding molecular weight of the primary fluid, Values are given in the following table and are shown graphically in Figure 10. Primary Fluid Steam Methanol Ethanol Benzene Triohlorethylene

M

N

18 32 46 78 131

-0.77 -0.62 -0.48 -0.33 -0.14

The equation of such a curve is of the form:

N

= C' X 10KM

On solution, the equation is found to be: N -10-0.0064'M

The relations for both self-entrainment and two-component entrainment may be brought together into a common relation which applies over the whole field of entrainment. Twocomponent relations differ from self-entrainment as a function of the molecular weights involved. I n self-entrainment the two-component entrainment formula takes the form:

-20.

=

cMN

where Go = molal self-entrainment M = molecular weight of both primary and secondary fluids

APRIL, 1939


473

THREE-STAGE STEAMJET VACUUM U N I T WITH BAROMETRIC INTERCONDENSERS USED FOR HANDLING705 POUNDS OF AIR PER HOUR AND WATER VAPORAT AN ABSOLUTE PRESSURE OF 5 MM.; THE VOLUMEOF VAPORS

ENTERING THISUNITIs OVER2,000,000 CUBIC FEETPER HOUR Courtesy, Croll-Reynolds Company

The ratio of molal entrainment of any substance to that of self-entrainment under the same conditions, &fi8, therefore equals ( v L / M )or ~ ( M / v L ) - ~ .I n order to test this relation, the values of all condensable fluids in two-component entrainment runs were computed a t entrainment pressures corresponding to C = 0.70. The average deviation of these values from the self-entrainment curve is +3.8 per cent, excluding the values computed for trichlorethylene. This substance deviates from normal on account of its low molal latent heat as compared with other substances and its tendency to decompose. Moreover, even an error of only 0.1 pound per square inch in the entrainment pressure may produce a n error in excess of 5 per cent in some of these trichlorethylene runs. When the number of factors involved in this correlation is considered, the correspondence between self-entrainment and two-component entrainment resulting from the correlating relation is close indeed. When air is used for secondary fluid, the results are somewhat erratic but are generally low. This is probably due to the tendency of air to cool the primary fluid which causes condensation and a corresponding loss of energy for compression. As the molecular weight of the primary fluid increases, this effect becomes more apparent and is probably due to a lower heat reserve in latent heat. With trichlorethylene as primary fluid it was almost impossible to maintain steady operating conditions when entraining air. Thus a relation has been developed for condensable vapors and applies over the whole range of operation of a n ejector over the range of conditions tested. It is necessary t o know only the entrainment relation for a single substance in self-entrainment when operating a given ejector a t a given ratio of Pb/Pa to define completely the characteristics with any other fluid or combination of fluids when operating under the same pressure ratio conditions. The experimental results may be interpreted by theoretical considerations into the possible mechanism of entrainment. According t o Mellanby (16) entrainment is probably due t o a tendency of the jet to overexpand on discharging from the nozzle. The secondary fluid leaks in a t the point of lowest pressure and is entrained by direct impact of the primary molecules. Once secondary molecules have penetrated into

the jet past its periphery, they are entrained and removed. They do not re-escape, for if they did they would force outer primary molecules with them. Consequently, entrainment may be measured by the ability of secondary molecules to penetrate into the jet under any given conditions. A simplified picture of entrainment may be formed by consideration of limiting conditions. The smallest conceivable molecule that might be used as a primary fluid would have a molecular weight approaching zero. Such a molecule would discharge from the nozzle a t a n infinitely high speed. A pressure differential between the surrounding atmosphere in the entraining chamber and the jet would be set up in accordance with Mellanby’s theory. This pressure differential would cause any secondary vapor to move inward a t a velocity depending upon its molecular characteristics. Resistance to flow inward would be caused by oblique impact of the outer jet molecules. The relative velocity of the secondary molecules inward, V , would measure the relative effectiveness in avoiding these impacts. The product of the velocity and the would then reprenumber of molecules traveling inward, sent the number which would be entrained. The velocity imparted to a vapor when expanded through a given pressure range and a given area is practically proportional to the square root of the reciprocal of the molecular weight, especially when the pressure differential is small:

z,

v

l/(m)1/2

The number of molecules which pass through that area per unit time is also proportional to the same factor:

u, E l/(m)1’2 Their product, V z is equal to l / m . Thus, if a molecule of negligible molecular weight were used as primary fluid, entrainment would be inversely proportional to the molecular weight of the secondary vapor. The other limiting primary molecule in entrainment would be one of infinite molecular weight. Such a substance would travel infinitely slowly so that any molecules in the surrounding atmosphere would come to static equilibrium with the jet molecules. Thus the partial pressure of all secondary


474

fluids within the jet would be the same when the pressure of the surrounding atmosphere is a constant. Under the same pressure conditions a given volume contains approximately the same number of molecules irrespective of molecular weight. Under these conditions molal entrainment would be the same for all secondary vapors. Between these limits, in the range of finite material, entrainment might be expected to vary continuously from one limit to the other as equilibrium is attained between the various factors involved over the whole range. The primary fluid supplies the momentum and energy necessary to entrain molecules of the secondary vapor

IS0

ASTEAM

METHANOL 0 ETHANOL A BENZENE

1

TRICHLORETHYLENE

0

feu,

Y

0.10 MOLECULAR WEIGHT

OF

PRIMARY FLUID

OF EXPONENT N WITH THE MOLECUFIGURE 10. VARIATION LAR WEIGHTOF THE PRIMARY FLUID

which are entrained when they penetrate the jet of primary vapor. The faster this travels, the.faster are the secondary molecules removed and the greater is the pressure differential produced, provided the fluid streams conform to the ejector openings. The greater this pressure differential, the greater is the tendency of the secondary molecules to acquire velocity head and to penetrate the jet. When this occurs, the demands upon the jet are increased in supplying energy for entrainment and compression. This tends to slow the jet until a balance between all factors is attained. I n self-entrainment the efficiency of entrainment and compression is the same for all fluids when operating under fixed pressure conditions. Therefore, in this case the relative tendency of secondary fluids to penetrate the jet is the same for all fluids. However, when a light molecule is made to entrain a heavy one, the velocity of the primary fluid is so great relative to that of the heavy secondary fluid that impact and entrainment occur before the latter penetrates far into the jet. On the other hand, when light molecules are entrained, they travel into the jet a t a higher velocity and consequently penetrate more effectively. Thus more light molecules can be entrained under given pressure conditions than heavy ones. Since light primary molecules more nearly simulate the theoretical weightless particles than the heavy ones, a larger spread in the capacity to entrain various secondary fluids should be attained with light primary fluids. As the molecular weight of the primary fluid is increased, the spread should decrease until molal entrainment with very heavy primary fluids approaches a constant value for all secondary fluids, irrespective of their molecular weight. Thus the relations developed are partly justified by theoretical considerations which furnish a working picture of what possibly occurs within an ejector during entrainment.

VOL. 31, NO. 4

Interpretation of Experimental Work

It is interesting to interpret the factors involved in refrigeration in the light of the findings of this investigation, A primary consideration in refrigeration is the amount of cooling which can be produced by a given heat input or the heat efficiency of operation. I n the present steam-water vapor system this is limited to the status of development of ejector equipment. If factors such as flammability, chemical stability, and corrosion are for the moment neglected, it may be shown how the substitution of other fluids for steam affects the heat efficiency. Self-entrainment is the basis of all entrainment relations and so may be studied separately to advantage. Under a given ratio of boiler pressure to exhaust pressure, all fluids yield the same entrainment curve when the ratio of the amount of secondary fluid to primary fluid, w/W, is plotted against the value, C = (P, - Pe)/(Ps- Po). This relation may be developed from the correlation curves of Figure 7. The ratio w/W increases with decreasing values of C. The entrainment and exhaust pressures involved in C are different for every substance and are fixed by the desired refrigeration temperature and the available condenser temperature. The pressure a t zero entrainment may be determined from that of the reference substance by the relation developed in this study that a t a given ratio of Pb/Pn, irrespective of the absolute values of each, the over-all efficiency, Tb(Ts - TO)/Tz(Tb - To), is the same for all fluids. Since the ratio of the amount of secondary fluid entrained to the amount of primary fluid employed increases with decreasing values of C a t any given P,/P,, i t is desirable to operate a t low values of C. Thus for a fixed exhaust pressure the entrainment pressure should be relatively high and the pressure a t zero entrainment should be relatively low. This is a function of ejector design and the properties of the fluids. I n general those substances with low atmospheric boiling points exhibit this desired characteristic in their vapor pressure curves. Hence, from this standpoint steam is not a very suitable refrigerant for attaining low temperatures in self-entrainment. Because of the difficulty of maintaining very high vacuum against leakage, it is obviously advantageous to operate the evaporator a t somewhat higher pressures than that possible in the steam system. However, the relations developed show that when the exhaust pressure is increased, the boiler pressure must be increased proportionately for equal efficiencies. When a too low-boiling compound is used in self-entrainment, the boiler pressure may become excessive. This was also indicated in the work of Kalustian in his analysis of a theoretical ammonia system (11). He assumed that all fluids would operate with equal effectiveness in self-entrainment in an ejector but gave no basis for this assumption. That i t is justified is demonstrated by the findings of the present study. Thus a balance of boiler pressure and refrigeration temperature must be attained in order that a self-entrainment system might have a high efficiency. It is not expected that a great improvement can result by substitution of other substances in self-entrainment for steam; and when other factors such as flammability, corrosion, chemical stability, and cheapness of refrigerant are taken into consideration, the advantages are largely with steam. It is in the field of two-component entrainment that advantages in the proper selection of substances may accrue. The relation between self-entrainment and two-component entrainment under uniform conditions developed in this study can be expressed by the equation: Ga/Ga = ( M / m ) - N where 2oz/20s = ratio of amount of molal entrainment of any secondary vapor by any primary vapor relative to that of self-

APRIL, 1939


entrainment of primary fluid under the same conditions of operation N = exponent dependent upon molecular weight of primary fluid Because of the functional relation between N and M , the molal ratio is dependent not only on the molecular weight ratio, but on the molecular weight of the primary fluid. The variation of the molal ratio with the molecular weight of the primary fluid when entraining several secondary fluids used in this study is shown graphically in Figure 11; corresponding calculated values are as follows: Primary Fluid Steam Methanol Ethanol Benzene CaHClr

M 18 32 46 78 131

N -0.77 -0.62 -0.51 -0.32 -0.14

-

Z / w a When Sea. Fluid Is:Steam Methanol Ethanol Benzene CnHCls 0.32 0.21 0.64 0.49 1.00 0.42 0.80 0.58 1.00 1.43 0.76 0.59 1.20 1.00 1.61 0.85 1.18 1.00 1.60 1.33 1.08 1.00 1.16 1.32 1.22

d

Each curve represents the entrainment of a single secondary fluid by various primary fluids. It is noted that G=,& increases with decreasing molecular weight of secondary fluid for all primary fluids, and that all the curves reach a maximum molal ratio when operating with a primary fluid of fixed molecular weight. For example, if a vapor with a molecular weight of 18 is entrained by a primary fluid with a molecular weight of about 61, the amount of molal entrainment of this secondary fluid is a maximum and is about 64 per cent in excess of that which might be entrained in self-entrainment of the primary fluid. On the other hand, if a secondary fluid with a molecular weight of 78 is entrained a t maximum efficiency, only an 8 per cent increase in effectiveness is experienced over the self-entrainment case. I n establishing the curves of Figure 11 and obtaining maximurn values, several intermediate molecular weights of the primary fluid were assumed for purposes of computation, and calculations were made using values of N as read from the curve of Figure 10. For values above a molecular weight of 150 of the primary fluid, the curve of Figure 10 was extrapolated as a straight line, and the values of N so obtained were used in computations. Of somewhat less practical importance but of theoretical significance are several other characteristics indicated by these curves. As the molecular weight of the secondary fluid increases, the maximum occurs with primary fluids of higher molecular weights. I n addition, the rate of change of the molal ratio with the molecular weight of the primary fluid on both sides of the maximum points decreases most rapidly with secondary fluids of low molecular weight. Thus the latter are more sensitive to change in the molecular weight of the primary fluid in entrainment than are secondary fluids of high molecular weights. If the maximum points are connected, they fall upon a continuous curve which is asymptotic to the axes, W,/W. = 1.00 and M = 0. In considering the limiting types of primary fluids which might be used in entrainment, the entrainment of all secondary vapors was shown to approach a constant value as the molecular weight of the primary fluid increased to very large values. This is indicated in the dotted portions of the curves (Figure 11) which were obtained by calculation from a n extrapolation of the curve of Figure 10 into the region of high molecular weight. I n the other limit, as the molecular weight of the primary fluid approaches very small values, the results are not indicated on Figure 11. However, it may readily be seen that the maximum value of G/G approaches infinity under these conditions. The advantage of selecting the proper molecular weights in obtaining high efficiency of operation is obvious from the foregoing analysis, but other factors come into play in a

475

choice of fluids. By using two fluids, the value of C can be decreased to the minimum and thus the equivalent molal self-entrainment ratio, W,/W,, can be increased to a maximum. C equals ( P,- P,)/(P, - Po), which varies inversely with the ratio ZOa/Wa. I n a two-component system the exhaust pressure, P,, which corresponds to the available condenser temperature, is determined by the properties of the fluids used. If the two fluids are immiscible, the saturation pressures are additive; and if they are miscible, the pressure is determined by the composition of the condensate. All other factors being equal, it is desirable to employ the second type of system which tends to decrease the exhaust pressure and hence the ratio of compression which measures the energy demand for compression. I n order to decrease C, a secondary fluid may be chosen which has a n entrainment pressure corresponding to the desired refrigeration temperature as near the exhaust pressure as possible-i. e., a substance with a vapor pressure curve showing a rapid change of temperature with pressure in the range of operation. I n regard to the primary fluid, it should have a characteristic of as large a pressure differential between the exhaust pressure and the pressure a t zero entrainment as possible. These can both be controlled by the proper choice of boiler and evaporator compounds.

SECONDARY FLUIDS A STEAM METHANOL o ETHANOL 4 BENZENE

.

-

18

32 46 78

m TRICHLPRETHYLEYE 131

x MAXIMUM VALUES lU3

150

200

2

MOLeCULAR WEIGHT OF PRIMARY FLUID

FIGURE 11. CORRELATION OF RELATIVE ENTRAININ TWO-COMPONENT AND SELF-ENTRAINMENT SYSTEMS

MENT

A further advantage may be secured by the selection of fluids on the basis of thermal properties. The heat absorbed per unit of secondary material moved must of necessity be high. Thus a substance of high molal latent heat should be selected. For purposes of comparison of molal latent heat, the approximate values measured by the Trouton constant can be used to advantage. When the secondary fluid is the volatile constituent in a solution, the heat of solution absorbed on evaporation can also serve in cooling, and the use of this type of evaporator fluid has distinct possibilities. The primary fluid, on the other hand, should require a low

476


VOL. 31, NO. 4

of compression to heat input. Therefore, i t should have a low liquid speTO),is a single cific heat and a low function of the ratio of boiler to exhaust. T r o u t o n constant. pressures for all vaI n addition, the pors; a maximum efmolec u l a r weight ficiency is reached a t should be as low as a definite pressure ratio corresponding possible to be conto minimum suction sistent with a favorpressure. able molecular 4. In self-entrainweight ratio because m e n t t h e weight ratio of secondary the heat input revapor entrained to quirement increases primary vapor emwith molecular ployed, w / W , is the Courtesy, Croll-Reynolds Company weight w h e n t h e same for all vapors A 7200-SQUARE-FOOT HEATEXCHANGER BUILTINTEGRAL WITH A VACUUM a t a given ratio of fluids h a v e a b o u t TO PRODUCE 300 TONSOF REFRIGERATION AT 40 ’ F. CHAMBER DESIGNED pressures, P b / P z , the same liquid speWHENCONNECTED TO SUITABLE STEAMJETVACUUM EQUIPMENT when t h e entraincific heats. ment pressure is seAn additional relected as a function of both the suction pressure at zero entrainment and the exquirement in refrigeration in two-component systems should haust pressure. A function which may be employed to adbe noted. The saturation pressure of the primary fluid over vantage in establishing the entrainment pressure is given by the range of compression should be lower than that of the the equation: C = ( P x - P , ) / ( P , - Po). When Pb/Pz and secondary vapor. If this pressure is higher, it may be imC are fixed, the efficiency of expansion, entrainment, and compression in any ejector is the same for all vapors in self-enpossible to attain the entrainment pressure or to attain it trainment. only at low efficiencies because of the relatively high operat5 . In two-component entrainment, which includes selfing pressures of the primary fluid used. entrainment as a special case, the amount of molal entrainment This outline serves to indicate the most favorable charof any secondary fluid effected by any condensable primary fluid may be expressed by the equation: ‘iii = cmN, where exponent N acteristics which should be sought in the selection of vapors = -lO-O.O064M and constant c varies with the conditions of for two-component entrainment. It is realized that a system operation and the design of the ejector. which takes advantage of them all in the highest degree 6. In correlating two-component entrainment with self-would be almost impossible of realization. However, a field entrainment, the ratio of the amount of molal entrainment of any secondary fluid by any primary vapor to that of self-entrainfor research has been opened for the development of this type ment of the primary vapor under the same conditions is given of system, and the direction in which improvement may lie by the equation GB/Zs = ( M / m ) - N where the variation of the has been indicated. I n addition to the problem of selecting molal ratio shows striking characterietics for the different molecufluids for favorable heat efficiencies, other problems remain. lar weight combinations. These include flammability, which may or may not be a a. When a single secondary fluid is entrained by a number of primary vapors, the molal ratio increases with increasing serious hazard according t o the service; but the use of a molecular weight of primary vapor until a maximum is atflammable substance in the boiler is dangerous whereas in the tained. Further increase in molecular weight of the primary evaporator it may be satisfactory. Others include chemical vapor causes a decrease in the molal ratio until, with very stability, toxicity, and corrosion. heavy primary vapors, a ratio of 1.00 is approached. b. When a single primary va or is used to entrain a numWhen the most satisfactory system from a thermal standber of secondary fluids, the molar ratio increases with decreaspoint has been devised, the question of recycling the two ing molecular weight of the secondary fluids. fluids back to their respective units arises. This may be c. The maximum values of the molal ratios occur at inaccomplished by gravity separation with immiscible fluids, creasing molecular weights of the primary vapor as the molecular weights of the secondary fluid increase and tend to approach by separation of miscible fluids b y salting out one constituent a constant value of 1.00 a t very high molecular weights of the from the other, or by cycling the condensate into the evaporaprimary vapor. On the other hand, the maximum values tor at which point the volatile constituent is boiled away and tend to approach infinity as the molecular weights of the secthe residue is pumped to the boiler. The partial separation ondary fluid decrease to very small values. 7 . The factors inherent in an ejector refrigeration cycle indiof miscible constituents by discharging the mixture into a cate that, to be hi hly efficient from a thermal standpoint, a rectifying column also has possibilities. system should have fow molecular weights in a favorable molecular weight ratio as defined by the equation E& = (M/m)-N; it should employ a boiler fluid with a low heat input requirement, Conclusions with a relatively large pressure differential ( P x - PO)and with a boiling point higher than that of the evaporator fluid; and it 1. When the characteristics of an ejector are known for operashould use an evaporator fluid with a high latent heat and, if a tion with a single vapor, they may be determined for any other solution is involved, a high heat of solution with a relativelyvapor or for a two-component system by the relations estabsmall pressure differential ( P x - P#). lished in this study which apply completely over the ranges of pressure, temperature, molecular weight, and molecular volume investigated. Nomenclature 2. The variation of suction pressure with both boiler and c = constant exhaust pressures is approximately the same for all vapors, irC = term defined by ratio ( P , - P o ) / ( P l , PO) respective of molecular weight when operating under conditions E = efficiency of no entrainment. The suction pressure decreases with inH , = heat of compression, B. t. u./lb. creasing boiler pressure and fixed exhaust pressure a t a variH e = heat of expansion, B. t. u./lb. able rate down t o the critical pressure ratio and then continues t o J = Joule’s constant, 778 ft.-lb./B. t. u. decrease a t a constant rate until a minimum suction pressure is K = constant attained, which is approximately the same for all vapors; beyond m = molecular weight of secondary fluid this point the suction pressure increases with increasing boiler M = molecular weight of primary fluid pressure. N = exponent in equation U, = cmN 3. The over-all efficiency of an ejector under conditions of P = pressure, lb./sq. in. absolute no entrainment as expressed by the ratio of the Carnot efficiency

APRIL, 1939


R = gas constant s = ratio of specifiz heats T = temperature Rankine v = velocity, ft.fsec. w_ = secondary fluid, lb./hr. w = secondary fluid, lb. moles/hr. iL/T& = ratio of molal entrainment of any substance to that of self-entrainment under the same conditions W = primary fluid, lb./hr. W = primary fluid, lb. moles/hr. y = reheat, yo A = difference Subscripts : 6 = boiler conditions e = entrainment conditions 0 = suction conditions at zero entrainment x = exhaust conditions

Literature Cited (1) Bancel, Trans. Am. Inst. Chem. E n g r s . , 30, 136 (1933). (2) Barnard, Ellenwood, and Hirschfeld, “Heat Power Engineering,”Vol. I11 (1933). (3) Copley, Simpson, Tenney, and Phipps, Rev. Sci. Instruments, 6, 265-7 (1935). (4) Edwards, Ibid., 6, 145-7 (1935).

477

Air Conditzoning, 5, 77-81, 147-8 (1933). (6) Foster Wheeler Corp., Catalog 116B (1927). (7) Goodenough, Power, 66, 466-9 (1927). (8) Graham and Kooistra, Heating & Ventzlating, 30, 22-7 (1933). (9) Ho, Rev. Sci. Instruments, 3, 133-5 (1932). (10) Jackson, IXD.ENG.CHEM.,28, 522-6 (1936). (11) Kalustian, Refrig.Eng., 28, 188-93 (1934). (12) Kaula and Robinson, “Condensing Plant,” 1926. (13) Klumb and Glimm, Phvsik, Z.,34, 64-5 (1933). (14) Marks, Mechanical Engineers’ Handbook, 1930. (15) Mellanby, Trans. Inst. Chem. Engrs. (London), 1928, 66-84. (16) Morgan, Power, 78,454-6,506-7 (1934). (17) Natl. Bur. Standards, Circ. 394 (1931). (18) Natl. Bur. Standards, Tech. Paper 193 (1921). (19) Parr and Baumeister, Psychrometric Tables and Charta for Air-Water Vapor Mixtures, 1928. (20) Schutte and Koerting Go., Bull. 5H, Vol. 2 (1930); 4E, Vol. 1 (1931). (21) Sim, “Steam Condensing Plant,” 1925. (22) Stodola (tr. by Lowenstein) “Steam and Gas Turbines,” Vol. (1927). (23) Vivian, Compressed A i r Mag., 38, 4141-6 (1933). (24) Waterfill, Refrig. E n g . , 24, 137-42 (1932). (25) Watson, Engineering, 1933, 230-2, 255-7, 262-5; Proc. Inst. Mech. Engrs. (London), 124,231-300 (1933). (26) Whitney, Refrig’. Eng., 24, 143-6 (1932). (27) Zabel, Rev. Sci. Instruments, 6, 54-5 (1935). ( 5 ) Fleisher, Heating Piping

FLUID RESISTANCE IN PIPES M. P. O’BRIEN, R. G. FOLSOM, AND FINN JONASSEN University of California, Berkeley, Calif.

T

HE theoretical work of von KBrmBn, Prandtl, and G. I.

Taylor, and the experiments of Hopf, Fromm, Nikuradse, Schiller, and others have explained many features of the phenomenon of turbulent flow and have led to a number of important practical applications. The original impetus for the study of fluid resistance was the necessity for accurate prediction of the loss of head in pipes, and it is of interest to consider the extent to which the turbulence theory and substantiating experiments have advanced our knowledge of this important engineering problem. Reference is frequently made in the literature to smooth pipes and rough pipes. Originally the terms “smooth” and “rough” referred simply to the physical characteristics of the pipe walls, but in recent years they have acquired a dynamic significance. If a pipe is smooth in the hydraulic sense, the resistance coefficient in turbulent flow is affected by the viscosity but not by small changes in surface roughness. More specifically, a pipe is “smooth” if the friction coefficient plotted as a function of Reynolds number foIlows a certain curve obtained from tests on brass, lead, and other visually smooth surfaces. A pipe is “rough” if its friction coefficient is independent of the viscosity-that is, if the coefficient is a constant on the Reynolds number diagram. This condition of a constant f is also referred to as fully developed turbulence. Thus the same pipe may be smooth under one set of flow conditions and rough under another. Between rough and smooth in this dynamic sense lies almost the entire range of flow conditions that are of engineering importance. This paper will consider the extent to which present concepts of the nature of fluid resistance permit prediction of the head loss in this transition zone.

Smooth Pipes Von KArmBn’s theory of the local similarity of the flow pattern in the central core of any turbulent flow (7, 8, 9) leads to an equation for the relative velocity distribution which has been found to agree with experiment. A further assumption regarding the effect of the traction a t the wall of a smooth pipe gives the form of the equations for both the absolute velocity throughout the cross section and the friction

Formulas based on the theory of fully developed turbulent flow and on experiments using artificially roughened pipes are applied to extrapolated data for commercial pipes in order to obtain the equivalent roughness. Using this roughness, it is found that clean pipes do not follow a curve similar to that of Nikuradse in the transition zone between rough and smooth flow conditions. The conclusion is drawn that the turbulence theory has not yet provided a reliable generalized treatment of pipe resistance in the region important in engineering problems.

Performance of Ejectors As a Function of the Molecular Weights of

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